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Question

If y+za=z+xb=x+yc then show that xb+ca=yc+ab=za+bc

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Solution

y+za = z+xb = x+yc = K

(y+z)=ak,(z+x)=bk,(x+y)=ck

b+c-a = 1k(z+x+x+yyz) = 2xk

c+ab=1k(x+y+y+zx)=2yk

a+3c=1k(y+z+z+xxy)=2zk

xb+ca=x2x/k=k/2

yc+ab=k/2=za+bc=xb+ca


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